The present invention relates in general to three-dimensional (3-D) display of tomographic data, and more specifically to producing artifact-free images using the dividing cubes method for extracting surface definitions from tomographic data.
Tomographic medical imaging employs the collection of data representing cross sections of a body. A plurality of object interrogations can be processed mathematically to produce representations of contiguous cross-sectional images. Such cross-sectional images are of great value to the medical diagnostician in a non-invasive investigation of internal body structure. The technique employed to collect the data is a matter of indifference to the present invention. Any technique such as, for example, X-ray computed tomography, nuclear magnetic resonance tomography, single-photon emission tomography, positron emission tomography, or ultrasound tomography may serve equally.
A body to be imaged exists in three dimensions. Tomographic devices process data for presentation as a series of contiguous cross-sectional slices along selectable axes through the body. Each cross-sectional slice is made up of a number of rows and columns of voxels (parallelepiped volumes with certain faces corresponding to pixel spacing within each slice and others corresponding to slice spacing), each represented by a digitally stored number related to a computed signal intensity in the voxel. In practice, an array of, for example, 64 slices may each contain 512 by 512 voxels. In normal use, a diagnostician reviews images of a number of individual slices to derive the desired information. In cases where information about a surface within the body is desired, the diagnostician relies on interferences of the 3-D nature of the object derived from interrogating the cross-sectional slices. At times, it is difficult or impossible to attain the required inference from reviewing contiguous slices. In such cases, a synthesized 3-D image would be valuable.
Synthesizing a 3-D image from tomographic data is a two-step process. In the first step, a mathematical description of the desired object is extracted from the tomographic data. In the second step, the image is synthesized from the mathematical description.
Dealing with the second step first, assuming that a surface description can be synthesized from knowledge of the slices, the key is to go from the surface to the 3-D image. The mathematical description of the object is made up of the union of a large number of surface elements (SURFELS). The SURFELS are operated on by conventional computer graphics software, having its genesis in computer-aided design and computer-aided manufacturing, to apply surface shading to objects to aid in image interpretation through a synthesized two-dimensional image. The computer graphics software projects the SURFELS onto a rasterized image and determines which pixels of the rasterized image are turned on, and with what intensity or color. Generally, the shading is lightest (i.e., most intense) for image elements having surface normals along an operator-selected line of sight and successively darker for those elements inclined to the line of sight. Image elements having surface normals inclined more than 90 degrees from the selected line of sight are hidden in a 3-D object and are suppressed from the display. Foreground objects on the line of sight hide background objects. The shading gives a realistic illustion of three dimensions.
Returning now to the problem of extracting a mathematical description of the desired surface from the tomographic slice data, this step is broken down into two subtasks, namely the extraction of the object from the tomographic data, and the fitting of the surface to the extracted object. A number of ways are available to do the first subtask. For example, it is possible to search through the signal intensities in the voxels of a slice to discern regions where the material forming the object has sufficient signal contrast with surrounding regions. For example, signal intensities characteristic of bone in X-ray computed tomography have high contrast with surrounding tissue. A threshold may then be applied to the voxels to identify each one in the complete array lying in the desired object from all voxels not in the object.
Referring now to the second subtask, one technique for fitting the 3-D surface to the extracted object is known as the dividing cubes method which is disclosed in commonly assigned U.S. patent application Ser. No. 770,164, filed Aug. 28, 1985, U.S. Pat. No. 4,719,585 which is hereby incorporated by reference. By the dividing cubes method, the surface of interest is represented by the union of a large number of directed points. The directed points are obtained by considering in turn each set of eight cubically adjacent voxels in the data base of contiguous slices. Gradient values are calculated for the cube vertices using difference equations. If the surface passes through a cube, then it is subdivided to form a number of smaller cubes, referred to as subcubes or subvoxels. By interpolation of the adjacent point densities and gradient values, densities are calculated for the subcube vertices and a gradient is calculated for the center of the subcube. The densities are tested (e.g., compared to a threshold). If some are greater and some less than the threshold, then the surface passes through the subcube. In that case, the location of the subcube is output with its normalized gradient, as a directed point. It is also possible to define the surface using a range of densities (e.g., an upper and lower threshold). The union of all directed points generated by testing all subcubes provides the surface representation. The directed points are then rendered (i.e., rasterized) for display on a CRT, for example.
Increasing the number of data points by interpolating into subcubes gives smooth, high resolution images. It is apparent from the above-mentioned application that dividing cubes avoids scan conversion by matching subcube faces to the pixel resolution of the display, thus greatly simplifying rendering.
Various tradeoffs become apparent as the degree of interpolation performed (i.e., subcube size) is varied. It should be noted that large cubes are typically subdivided only by positive integer amounts along each axis, though not necessarily the same integer for different axes. As interpolation increases and subcube size decreases along an axis, image quality (e.g., resolution and smoothness) can be increased. However, since the number of data points increases, more storage, processing hardware, and processing time are required. Therefore, the subcubes should be as large as possible without adversely affecting image quality.
In interactive graphics systems, an operator can perform various functions on the image, such as scaling (or zooming) and rotation, thereby defining a viewing perspective. These functions are typically achieved using a Current Transformation Matrix (CTM) that operates on the data in a renderer before being sent to the display.
A further consequence of the amount of data interpolation relates to the appearance of image artifacts at certain rotational positions. Thus, a set of directed points may have sufficient interpolation to view the object from one angle, but not enough for another viewing angle. The image artifact usually encountered is a structured pattern of holes in the image.
Accordingly, it is a principal object of the present invention to provide artifact-free images while minimizing data-handling requirements and the amount of computations.
It is a further object of the invention to minimize the number of directed points generated by the dividing cubes method of extracting a surface definition from 3-D tomographic data.
It is still another object to eliminate holes in an image resulting from insufficient interpolation.